US President George W Bush has said the US-led security push in the Iraqi capital, Baghdad, will take "months, not days or weeks" to show results.
US patrols have been venturing out on foot in Baghdad
In a speech to mark four years since the 2003 invasion, he said those on the ground were seeing "hopeful signs".
But he warned it would be disastrous for US security if Washington decided it was best to "pack up and go home".
His comments came as a BBC/ABC News poll suggested Iraqis are increasingly pessimistic about the future.
Less than 40% of those polled said things were good in their lives, compared to 71% two years ago.
However, a majority said that, despite daily violence, they did not believe Iraq was in a state of civil war.
Other key findings from more than 2,000 people who took part in the poll:
- 58% overall said they wanted Iraq to remain a unified country
- Almost all said they did not want Iraq to be broken up along sectarian lines
- Only 35% said foreign troops should leave Iraq now
- A further 63% said foreign troops should go only after security has improved.
Monday saw 14 people killed in the northern city of Kirkuk when at least eight bombs went off in the space of an hour. And an attack by the entrance to a Shia mosque in Baghdad killed at least five.
Iraqi Prime Minister Nouri Maliki insisted that the sectarian conflict in Iraq was ending, in an interview with British broadcaster ITV.
Despite Sunni-Shia violence, Mr Maliki believes the biggest threat to peace in Iraq is from al-Qaeda.
'Good days and bad days'
"Four years after this war began, the fight is difficult, " President Bush said in his eight-minute speech from the White House.
He said his plan to send 28,000 extra US troops to secure Baghdad and the western Anbar province "will need more time to take effect".
"There will be good days and bad days ahead as the security plan unfolds," he said.
He said although it might be tempting to look at the challenges and decide that the best option would be to pack up and go home, "the consequences for American security would be devastating".
"If American forces were to step back from Baghdad before it is more secure a contagion of violence could spill out across the entire country. In time this violence could engulf the region.
"The terrorists could emerge from the chaos with a safe haven in Iraq to replace the one they had in Afghanistan which they used to plan the attacks of September 11, 2001. For the safety of the American people we cannot allow this to happen."
He said aggressive operations were being carried out against both Shia and Sunni militants, and against al-Qaeda.